Gravity had some scenes filmed underwater, but water causes challenges for lighting. This is a list question, because there is no right answer and movie directors will implement the effect anyway they can. It's a challenge to do it better than the previous space movie.
– ReactgularOct 22 '13 at 14:48

The rotating sets in 2001 were created to make the actors look like they were walking with magnetic boots (when in the transport craft), and to show Dave jogging around the crew cabin. The other actor was strapped to his chair as the entire set rotated. Very cool, but not to simulate weightlessness more like simulated gravity.
– ReactgularOct 22 '13 at 14:42

@MathewFoscarini that's just a part of the answer, just used to present one more example.
– Ankit SharmaOct 22 '13 at 17:54

Inception is well known for simulating all of its zero/reduced gravity scenes without CG.

There is a behind the scenes documentary where the effects team detail the various method they use – and crucially how different shots within a sequence use different methods. This means there's never a single "trick" that the eye can catch to break the immersion.

Christopher Nolan: We did it through a number of different rigs and in the final edit what you see is shot to shot to shot it tends to be a different orientation and a completely different rig in each shot and I think that more than anything else really stops the audience of seeing the trick of how this scene is done.

They used different sets for the scene, with different orientations, suspending the actors on wires to let them "fly" through the scene. The long hotel corridor was built upright, so that the walkway was vertical and the camera is looking upward from the bottom. Then they hung the actors upside down so they can freely move towards the sides of the corridor.

Paul Franklin: The vertical corridor is supposed to be the same location as the horizontal corridor, it's an identical set. The difference is that it has been built vertical standing on its end. This means we drop actors and stunt performers on wires down into the set and the camera looks up at them. They can then be raised and lowered and swing around the sides and it looks like they're floating in zero gravity.

The actors also tried to simulate the behaviour of weightless people, based on real examples.

Joseph Gordon-Levitt: In real zero-G, and I've actually spoken to people that have been in real zero-G, what they told me is they never felt so relaxed in life. What I did is the exact opposite of that. In order to make it look like that was the case I actually had to keep every muscle tight because I was supporting myself.

I think that there's really only one method to simulate weightlessness in that excellent documentary. The other methods deal with shifting gravity. Please consider adding an explanation of what they do in your answer as the video might not always be available.
– coleopteristOct 22 '13 at 15:35

The old video link didn't seem to work, so I linked to it on YouTube. I also tried to elaborate on what the video actually contained to make it more than a mere link-only answer and justify its votes a bit more.
– Napoleon Wilson♦Nov 11 '16 at 16:30

Please try to describe what they did in a little more detail. The article might not always be available or available for free. (I haven't clicked the link yet as I haven't watched Gravity yet.)
– coleopteristOct 23 '13 at 3:00

More recent films also use digital doubles to animate all but actors' faces. This was used extensively on Ender's Game, and to some extent on Gravity. Per this article:

To create a sense of weightlessness, the filmmakers shot actors in
harnesses and on wires against a greenscreen set to place them in a
virtual world. Then to achieve the look of zero-G — and obey the laws
of physics — visual effects studio Digital Domain ultimately retained
only the actor’s faces and relied instead on digital doubles of their
bodies for the sequence.

Nearly all the digital doubles created for Ender’s Game were in the
zero-G Battle Room. . . . Digital Domain’s animation team developed
tools that allowed artists to correct for that movement, then
re-projected digital doubles (or parts of their bodies) back into the
shots. Because Digital Domain had developed CG versions of the actors’
flash suits and re-created the lighting environment digitally, they
were able to keep the actors’ faces from the live action shoot and
replace nearly all of the body motions with digital doubles.

If you are looking for a low-budget option, it is worth doing a YouTube search for Anne Hathaway's zero-gravity move on the Graham Norton Show. She demonstrates how, when filming Interstellar, actors were required to simulate weightlessness by standing on one leg. She stands on one leg with a relaxed knee and extends the other leg behind her so that it looks like it is floating on camera. It is a surprisingly effective technique, with zero-budget.

Director Ron Howard describes other techniques in his commentary for Apollo 13 for simulating weightlessness in scenes shot on the soundstage. The actors often sat one one end of a see-saw which was weighted on the other end, allowing them to bob up and down smoothly. Simple camera tricks were used such as having the actors lay down on their sides opposite each other, and turning the camera 90 degrees to making it appear that one actor was completely upside down. Also, they filmed the scenes in the KC-135 before the soundstage ones so the actors knew what real weightlessness looked and felt like, and they could more easily fake the look on earth.